{"paper":{"title":"Bound states for the magnetic Neumann Laplacian in planar sectors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Ayman Kachmar, Mikael Sundqvist","submitted_at":"2026-07-14T10:19:18Z","abstract_excerpt":"We study the magnetic Neumann Laplacian in an infinite planar sector of opening $\\alpha\\in(0,\\pi)$ under a constant magnetic field. Building on earlier work by Bonnaillie-No\\\"el and collaborators and by Exner, Lotoreichik, and P\\'erez-Obiol, we prove that the bottom of the spectrum lies strictly below the half-plane threshold for every convex sector. Consequently, $H_\\alpha$ has a discrete ground-state eigenvalue for every $0<\\alpha<\\pi$. This resolves the bound-state problem for convex sectors, a model problem arising in the analysis of magnetic localization near corners and of the third crit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12600","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.12600/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}